import numpy as np, pandas as pd, matplotlib.pyplot as plt

P = np.array([[0.7, 0.3], [0.4, 0.6]])
V = np.array([1.0, 0.0])
traj = [V @ np.linalg.matrix_power(P, t) for t in range(20)]
df = pd.DataFrame(traj, columns=["State A", "State B"])

df.plot(title="MDP State Transition Trajectory")
plt.xlabel("Time Step")
plt.ylabel("Probability")
plt.show()